The equation of a parabola

Name: Ian Forsyth
Who is asking: Student
Level: Secondary

Question: Given the points A(0,0) B(60,10) C(24,d) find the equation of the parabola. leave the equation in terms of x, y and d if the general form of a quadratic is y = ax² + bx + c.

Note: B(60,10) is not a turning point

Hi Ian,

I assume that you want the parabola that passes through A, B and C. If the parabola passes through a point then the coordinates of the point satisfy the equation of the parabola.

Substituting A, B and C into the equation of the parabola gives

0 = a 0² + b 0 + c
10 = a (60²) + b 60 + c
d = a (24²) + b 24 + c

The first equation implies c = 0 and the second and third equations become

10 = 60² a + 60 b
d = 24² a + 24 b

Solve these equations for a and b.

Cheers,
Penny Go to Math Central